An automated loading mechanism pushes a 40 \text{ kg} projectile along a horizontal guide … — Armed Services Vocational Aptitude Battery (ASVAB)

An automated loading mechanism pushes a $40 \text{ kg}$ projectile along a horizontal guide rail into a weapon system. The mechanism applies a constant forward force of $700 \text{ N}$ . If the sliding friction in the guide rail opposes the motion with a force of $100 \text{ N}$ , what is the acceleration of the projectile?

Answer: 15 m/s^2

Answer

The correct acceleration is found by first determining the net force acting on the projectile. Subtracting the

100 \text{ N}

of friction from the

700 \text{ N}

applied force yields a net force of

600 \text{ N}

. According to Newton's Second Law (

F = ma

), dividing this net force by the

40 \text{ kg}

mass results in an acceleration of

15 \text{ m/s}^2

Step-by-Step Solution

Calculate the net horizontal force acting on the projectile.

700 \text{ N} - 100 \text{ N} = 600 \text{ N}

The net force is the vector sum of all forces; friction directly opposes the forward applied force.

Use Newton's Second Law to set up the equation for acceleration.

a = \frac{F_{\text{net}}}{m}

Acceleration equals the net force divided by the mass of the object.

Substitute the known values into the equation.

a = \frac{600}{40} = 15 \text{ m/s}^2

Dividing the computed net force by the given mass provides the exact acceleration.

Key Concept

Newton's Second Law (F=ma) and Net Force

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